Matt Le Tissier has urged Southampton boss Ronald Koeman to sign striking reinforcements before the transfer window closes.
Tottenham will allow Emmanuel Adebayor and either Younes Kaboul or Vlad Chiriches to leave on loan before the deadline.
Lewandowski revealed his desire to join the German and European champions over the summer, but accepted he would have to remain at Dortmund until next year when his contract expires.
The 25-year-old has reportedly already agreed terms on next summer's switch to the Bavarian club and had no reservations in making his intentions clear.
When asked by SPORT1 television channel whether he could announce his switch to Bayern, the Poland international responded: "Yes, because then I can officially sign a contract."
Lewandowski was a pivotal player for the Westphalians as they finished runners-up to Bayern in both the domestic and European leagues last season.
The forward scored 36 goals in all competitions, which included becoming the first player to score four times in a semi-final of the Champions League when he single-handedly dismantled Real Madrid.
He was unable to fire Dortmund to victory in the final, though, as Bayern claimed a 2-1 win at Wembley thanks to a last-gasp Arjen Robben goal.
Bayern made a bid for the striker over the summer but Dortmund were steadfast in their refusal to sell Lewandowski, who was also linked with Real Madrid, Chelsea and Manchester City, to their fierce rivals.
And while Lewandowski was unhappy with the decision, he has made clear his interest in letting the final year of his contract with Dortmund run out before joining Bayern.
He has scored four goals this season to help Dortmund to the top of Bundesliga after six games, level on 16 points with Bayern.